Mixing
What is the precise definition of the prefix “co” in mathematics?
$begingroup$
Given a notion "A" in mathematics, in many cases "coA" is also defined. Here are some common examples:
- sine and cosine;
- tangent and cotangent;
- secant and cosecant;
- function and cofunction;
- morphism and comorphism;
- functor and cofunctor;
- domain and codomain;
- limit and colimit;
- set and coset;
- product and coproduct;
- fibration and cofibration;
- homology and cohomology;
- homotopy and cohomotopy;
- prime and coprime;
- vector and covector;
and the list goes on. My question is, what is the generally accepted meaning of the prefix "co"? Given a mathematical notion "A", when is "coA"
also defined? Also, is "cocoA" always the same as "A"? (Here I am only asking about mathematical terminologies, so "coconut" does not count.)
Edit: Among all the examples listed above, the pair puzzles me the most is "set and coset". A coset is defined in the context of a subgroup of a group. I am wondering if there is any reason to call it a coset.
soft-question terminology
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
$endgroup$
|
show 11 more comments
$begingroup$
Given a notion "A" in mathematics, in many cases "coA" is also defined. Here are some common examples:
- sine and cosine;
- tangent and cotangent;
- secant and cosecant;
- function and cofunction;
- morphism and comorphism;
- functor and cofunctor;
- domain and codomain;
- limit and colimit;
- set and coset;
- product and coproduct;
- fibration and cofibration;
- homology and cohomology;
- homotopy and cohomotopy;
- prime and coprime;
- vector and covector;
and the list goes on. My question is, what is the generally accepted meaning of the prefix "co"? Given a mathematical notion "A", when is "coA"
also defined? Also, is "cocoA" always the same as "A"? (Here I am only asking about mathematical terminologies, so "coconut" does not count.)
Edit: Among all the examples listed above, the pair puzzles me the most is "set and coset". A coset is defined in the context of a subgroup of a group. I am wondering if there is any reason to call it a coset.
soft-question terminology
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
$endgroup$
1
$begingroup$
See cosine : etymology.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 14:52
2
$begingroup$
In most cases it's from the latin prefix 'com-', which means (usually) "together with". In the case of the trig functions it comes from the more specific latin 'complement' meaning it applies to another (complementary) side of the triangle.
$endgroup$
– Klaas van Aarsen
Feb 2 at 14:59
2
$begingroup$
Yes; I think that the moden ones are named so by analogy, to connote a couple of "complementar" concepts.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 15:00
4
$begingroup$
"A comathematician is a device for turning cotheorems into ffee." Some comathematician, I don't know . . .
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– Shaun
Feb 2 at 15:05
4
$begingroup$
+1 for the "coconut" non-example/
$endgroup$
– John Hughes
Feb 2 at 15:06
|
show 11 more comments
$begingroup$
Given a notion "A" in mathematics, in many cases "coA" is also defined. Here are some common examples:
- sine and cosine;
- tangent and cotangent;
- secant and cosecant;
- function and cofunction;
- morphism and comorphism;
- functor and cofunctor;
- domain and codomain;
- limit and colimit;
- set and coset;
- product and coproduct;
- fibration and cofibration;
- homology and cohomology;
- homotopy and cohomotopy;
- prime and coprime;
- vector and covector;
and the list goes on. My question is, what is the generally accepted meaning of the prefix "co"? Given a mathematical notion "A", when is "coA"
also defined? Also, is "cocoA" always the same as "A"? (Here I am only asking about mathematical terminologies, so "coconut" does not count.)
Edit: Among all the examples listed above, the pair puzzles me the most is "set and coset". A coset is defined in the context of a subgroup of a group. I am wondering if there is any reason to call it a coset.
soft-question terminology
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
$endgroup$
Given a notion "A" in mathematics, in many cases "coA" is also defined. Here are some common examples:
- sine and cosine;
- tangent and cotangent;
- secant and cosecant;
- function and cofunction;
- morphism and comorphism;
- functor and cofunctor;
- domain and codomain;
- limit and colimit;
- set and coset;
- product and coproduct;
- fibration and cofibration;
- homology and cohomology;
- homotopy and cohomotopy;
- prime and coprime;
- vector and covector;
and the list goes on. My question is, what is the generally accepted meaning of the prefix "co"? Given a mathematical notion "A", when is "coA"
also defined? Also, is "cocoA" always the same as "A"? (Here I am only asking about mathematical terminologies, so "coconut" does not count.)
Edit: Among all the examples listed above, the pair puzzles me the most is "set and coset". A coset is defined in the context of a subgroup of a group. I am wondering if there is any reason to call it a coset.
soft-question terminology
soft-question terminology
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
edited Feb 2 at 20:23
Zuriel
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
asked Feb 2 at 14:49
ZurielZuriel
1,9081228
1,9081228
1
$begingroup$
See cosine : etymology.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 14:52
2
$begingroup$
In most cases it's from the latin prefix 'com-', which means (usually) "together with". In the case of the trig functions it comes from the more specific latin 'complement' meaning it applies to another (complementary) side of the triangle.
$endgroup$
– Klaas van Aarsen
Feb 2 at 14:59
2
$begingroup$
Yes; I think that the moden ones are named so by analogy, to connote a couple of "complementar" concepts.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 15:00
4
$begingroup$
"A comathematician is a device for turning cotheorems into ffee." Some comathematician, I don't know . . .
$endgroup$
– Shaun
Feb 2 at 15:05
4
$begingroup$
+1 for the "coconut" non-example/
$endgroup$
– John Hughes
Feb 2 at 15:06
|
show 11 more comments
1
$begingroup$
See cosine : etymology.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 14:52
2
$begingroup$
In most cases it's from the latin prefix 'com-', which means (usually) "together with". In the case of the trig functions it comes from the more specific latin 'complement' meaning it applies to another (complementary) side of the triangle.
$endgroup$
– Klaas van Aarsen
Feb 2 at 14:59
2
$begingroup$
Yes; I think that the moden ones are named so by analogy, to connote a couple of "complementar" concepts.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 15:00
4
$begingroup$
"A comathematician is a device for turning cotheorems into ffee." Some comathematician, I don't know . . .
$endgroup$
– Shaun
Feb 2 at 15:05
4
$begingroup$
+1 for the "coconut" non-example/
$endgroup$
– John Hughes
Feb 2 at 15:06
1
1
$begingroup$
See cosine : etymology.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 14:52
$begingroup$
See cosine : etymology.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 14:52
2
2
$begingroup$
In most cases it's from the latin prefix 'com-', which means (usually) "together with". In the case of the trig functions it comes from the more specific latin 'complement' meaning it applies to another (complementary) side of the triangle.
$endgroup$
– Klaas van Aarsen
Feb 2 at 14:59
$begingroup$
In most cases it's from the latin prefix 'com-', which means (usually) "together with". In the case of the trig functions it comes from the more specific latin 'complement' meaning it applies to another (complementary) side of the triangle.
$endgroup$
– Klaas van Aarsen
Feb 2 at 14:59
2
2
$begingroup$
Yes; I think that the moden ones are named so by analogy, to connote a couple of "complementar" concepts.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 15:00
$begingroup$
Yes; I think that the moden ones are named so by analogy, to connote a couple of "complementar" concepts.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 15:00
4
4
$begingroup$
"A comathematician is a device for turning cotheorems into ffee." Some comathematician, I don't know . . .
$endgroup$
– Shaun
Feb 2 at 15:05
$begingroup$
"A comathematician is a device for turning cotheorems into ffee." Some comathematician, I don't know . . .
$endgroup$
– Shaun
Feb 2 at 15:05
4
4
$begingroup$
+1 for the "coconut" non-example/
$endgroup$
– John Hughes
Feb 2 at 15:06
$begingroup$
+1 for the "coconut" non-example/
$endgroup$
– John Hughes
Feb 2 at 15:06
|
show 11 more comments
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1
$begingroup$
See cosine : etymology.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 14:52
2
$begingroup$
In most cases it's from the latin prefix 'com-', which means (usually) "together with". In the case of the trig functions it comes from the more specific latin 'complement' meaning it applies to another (complementary) side of the triangle.
$endgroup$
– Klaas van Aarsen
Feb 2 at 14:59
2
$begingroup$
Yes; I think that the moden ones are named so by analogy, to connote a couple of "complementar" concepts.
$endgroup$
– Mauro ALLEGRANZA
Feb 2 at 15:00
4
$begingroup$
"A comathematician is a device for turning cotheorems into ffee." Some comathematician, I don't know . . .
$endgroup$
– Shaun
Feb 2 at 15:05
4
$begingroup$
+1 for the "coconut" non-example/
$endgroup$
– John Hughes
Feb 2 at 15:06